Learnable Group Transform For Time-Series

Romain Cosentino, Behnaam Aazhang

Keywords: Group Transform, Time-Frequency Representation, Wavelet Transform, Group Theory, Representation Theory, Time-Series

Abstract: We propose to undertake the problem of representation learning for time-series by considering a Group Transform approach. This framework allows us to, first, generalize classical time-frequency transformations such as the Wavelet Transform, and second, to enable the learnability of the representation. While the creation of the Wavelet Transform filter-bank relies on the sampling of the affine group in order to transform the mother filter, our approach allows for non-linear transformations of the mother filter by introducing the group of strictly increasing and continuous functions. The transformations induced by such a group enable us to span a larger class of signal representations. The sampling of this group can be optimized with respect to a specific loss and function and thus cast into a Deep Learning architecture. The experiments on diverse time-series datasets demonstrate the expressivity of this framework which competes with state-of-the-art performances.